Mathematical Foundations of Existential Coherence Theory

Mathematical Foundations of Existential Coherence Theory A Quantitative Framework for Universal Principles What if the fundamental patterns spanning physics, biology, and economics arise from seven simple axioms? This rigorous mathematical framework demonstrates that universal scaling laws emerge from logical necessity, not coincidence. Through formal proofs, we establish: • NULL is the only possible origin — any other beginning requires explanation• Systems stabilize at exactly √n diversity — a mathematical necessity, not optimization• Cooperation yields exponential returns (2^n) while competition remains linear (n)• Every network component becomes irreplaceable as complexity grows exponentially• The Higgs field serves as irreducible residue — preventing total cancellation to NULL Core Innovation: The Simplicity Formula (0 ≠ ∞) The universe exists in eternal tension between unreachable extremes. This boundary condition drives all dynamics and explains why complete systems require perpetual incompleteness. Falsifiable Prediction: Dark matter crystallization threshold at Σ*_crit = (124 ± 6) M☉ pc⁻² — derived from fundamental constants alone, with no free parameters. Empirical Validation: Dragonfly 44: Below threshold → 99% dark matter ✓ NGC 1052-DF2: Above threshold → ~0% dark matter ✓ Who This Is For: Theoretical physicists seeking unification frameworks Network scientists studying scaling laws across disciplines Cosmologists investigating dark matter distribution patterns Systems theorists exploring emergence and complexity Connection to Physics: Companion to "The Simplicity Theory" which provides the physical substrate (Urenergie dynamics) for these mathematical patterns. Technical Scope: Formal mathematical proofs, testable predictions, empirical validation protocols. This is mathematics, not metaphysics. Keywords: systems theory, network mathematics, NULL-origin, critical thresholds, dark matter, mathematical necessity, scaling laws Ready for: ArXiv submission, peer review, empirical testing Version 2.7 | Contact: [email protected] | Code: github.com/BrainyTX/simplicity-theory